Coupling of STAR-CCM+ to Other Theoretical or Numerical Solutions Milovan Perić
Contents • The need to couple STAR-CCM+ with other theoretical or numerical solutions • Coupling approaches: surface and volume coupling • Examples of surface and volume coupling • Future developments
Need for Coupling • Eliminate reflections from boundaries (especially inlet) • Reduce the size of 3D simulation domain (reduce computing cost, especially for long-lasting transient simulations) • Enable simulation of wave propagation over long distance (wake signature, shore impact etc.) Source: Wikipedia
Surface Coupling, I • An example of surface coupling is Fluid-Structure- Interaction (FSI): the solutions in fluid and structure are coupled at the contact surface… • The same approach can be applied to two fluid domains, whereas in each domain different equations (potential flow, Euler- or Navier-Stokes equations) can be solved with different methods (boundary element, finite element or finite volume). • There are many different options (implicit or explicit coupling, solving simultaneously for the whole domain or using solution in one subdomain to impose boundary conditions in another subdomain, one- or two- way…).
Surface Coupling, II • An example of surface coupling represents also the imposing of theoretical solution (Stokes 5 th -order wave, Pierson-Moskwoitz or Jon-Swap irregular long-crested waves, superposition of linear waves…) at an inlet boundary. • The imposed inlet values can also come from another numerical solution in the upstream subdomain. • The problem: reflection of upstream-traveling waves at such an inlet boundary if the coupling is only one-way.
Surface Coupling, III • An example of two-way surface coupling: The upstream domain imposes at interface inlet condition for the downstream domain; The downstream domain imposes at interface pressure- outlet condition for the upstream domain. • The most comprehensive approach: Solving for the same variables in the whole domain simultaneously (as we do with overset grids)… This fully-implicit approach requires exchange of information at each iteration within a time step… … and imposes some compatibility conditions…
Volume Coupling, I • Instead of using contiguous subdomains and coupling at a common surface interface, one can also use overlapping subdomains and enforce coupling over a volume zone… • The forcing is realized via a source term of the form: S * = - µ f ( ϕ - ϕ * ) where µ f is the forcing coefficient. • A large number is used when the variable value is to be fixed to ϕ * (e.g. dissipation rate at a near-wall cell).
Volume Coupling, II • A smoothly varying forcing coefficient provides also a damping function… µ f 3D Navier-Stokes Forcing zone 2D Euler • The volume coupling can also be either one-way or two- way (the forcing zones usually do not coincide)…
Volume Coupling, III • If the grids do not coincide, volume coupling requires interpolation of one solution to the other grid (mapping). • If the grid moves, this mapping has to be done in each time step… • … or even in each iteration, in the case of DFBI… • Volume mapping can thus be expensive!
Example from Technip, I Solution domain for 3D RANSE computation Solution domain for 2D Euler computation t = -17.33 s t = 0 s t = 1.16 s
Example from Technip, II • 3D-RANSE computation is performed only over the time 0 – 1.5 s in a domain 2 m long and 1 m wide around the cylinder. • 2D solution of Euler equations to obtain the desired wave at the cylinder position is performed over a 20 times longer solution domain (> 100 m) and over 20 times longer time period (ca. 20 s). • 2D Euler solution is used to initialize RANSE computation at the desired time, ignoring the obstacle (as we do with theoretical wave solutions). • Mapping 2D solution to 3D domain is much less expensive than 3D to 3D…
Coupling to Theory, I • Theoretical solutions can also be used for volume coupling… • Instead of specifying inlet conditions based on theory, one can use a forcing zone to impose theoretical solution in any part of the solution domain. • The advantage of this approach is that it provides damping both upstream and downstream of obstacles. • The disadvantage is that theory may not be a good representation of the solution of Navier-Stokes equations (e.g. linear wave theory)…
Coupling to Theory, II • Example: Stokes 5 th -order wave theory imposed at both inlet and outlet over forcing zones of different length… • Note: The computed wavelength is slightly shorter than theoretical, but the solution is forced to theory over a short distance (the forcing coefficient is too strong). Blue: Stokes theory (5 th order) Red: Computed Forcing zone Forcing zone
Coupling to Theory, III • 3D example: Flow around a vertical cylinder • The cylinder disturbs the free surface; disturbances propagate in all directions. • Inlet is relatively near cylinder – reflections can be better observed… • The solution domain is 9.2 m long and 6.4 m wide; cylinder diameter is 1 m and its axis is 3.8 m away from inlet. • Stokes wave parameters: wavelength 3.2 m, wave height 0.2 m, wave period 1.4043 s • The mesh is locally refined in free-surface zone and around cylinder (80 cells per wavelength and 20 cells per wave height). Forcing is applied all around cylinder …
Coupling to Theory, IV 1.6 m 1.2 m 2.4 m 1.6 m Grid in the free surface and the value of the forcing coefficient µ 0 : red means RANS-zone, blue means maximum forcing to Stokes 5 th -order theory. Outside zone around cylinder, the grid is only fine in x - and z -direction to resolve free surface variation – in y -direction it is coarse since the wave is long-crested.
Coupling to Theory, V Grid in the longitudinal section through the solution domain, also showing volume fraction distribution after 4 periods.
Coupling to Theory, VI Forcing Forcing Volume fraction of water in the longitudinal section through the solution domain, also showing the free surface shape from Stokes 5 th -order theory, after 4 periods. Note that the computed free surface position corresponds to the theory within forcing zones.
Coupling to Theory, VII Computation using standard approach in STAR-CCM+ (inlet + damping at outlet, symmetry conditions at sides) Volume fraction of water in the symmetry plane (upper) and side boundary (lower), also showing the free surface shape from Stokes 5 th -order theory, after 4 periods. Note that the computed free surface near inlet does not correspond to the theory, due to reflections.
Coupling to Theory, VIII Computation using inlet, damping at outlet, symmetry at sides Disturbances due to reflections at symmetry and inlet Computation using forcing (at inlet, sides and outlet) Free surface after 4 periods (around cylinder it looks the same) No obvious disturbances
Coupling to Theory, IX Animation of simulated free surface motion during the 3 rd and the 4 th period (using forcing). Along boundaries the free surface position corresponds to Stokes 5 th -order wave theory.
Coupling to Theory, X Animation of simulated free surface motion during the 3 rd and the 4 th period using the standard approach (inlet condition from Stokes 5 th -order theory, side boundaries are symmetry planes, outlet is pressure boundary set to represent flat free surface and damping is applied over 2.4 m towards outlet).
Coupling to Other Solutions, I • 2D example: Laminar flow of water around a circular cylinder in a channel, Reynolds number 200. • Boundary conditions: steady uniform flow at inlet, constant pressure at outlet. • Vortices are shed by the cylinder; pressure-outlet boundary condition is not optimal for outgoing vortices – disturbances occur… • The solution is forced into channel flow without obstacle over some distance towards outlet. • The aim of coupling to undisturbed channel flow is to avoid disturbances at outlet, i.e. to obtain an almost steady flow at outlet.
Coupling to Other Solutions, II 2D grid for the computation of unsteady laminar flow around cylinder in a channel (only part of the solution domain is shown – it is longer both upstream and downstream, with grid structure similar to what is seen here at both ends). The grid has 180 cells along cylinder perimeter and the thickness of the first cell next to wall is 1/166 th of the cylinder diameter. The time step was set to 120 steps per period of lift oscillation (on average 60 steps per period of drag oscillation). Under- relaxation factors were 1.0 for all transport equations and 0.5 for pressure.
Coupling to Other Solutions, III No forcing Forcing Drag force on cylinder: the result is practically identical, i.e. the forcing of the flow far away from cylinder does not influence the flow around cylinder (as far as drag and lift are concerned).
Coupling to Other Solutions, IV Animation of pressure variation: no forcing (upper) and with forcing (lower)
Coupling to Other Solutions, V Animation of velocity variation: no forcing (upper) and with forcing (lower)
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